Updating your Apple Watch with your iPhone is probably the easiest way to go. To make sure that your Apple devices have the latest bug fixes and security enhancements available, you need to keep your devices up to date. Some iOS updates might also require you to update watchOS. But in case you do not have access to your iPhone, you can update your iPhone through the following steps.
This would require that you update directly on your Apple Watch. If the Apple Watch has watchOS 6 or a later version, you’d be able to install updates without your iPhone.
To do that, you’d need to make sure that your watch is connected to Wi-Fi. On your watch, open the Settings app. Tap on General and then Software Update.
Tap Install if a software update is available, then follow the onscreen instructions to update. Through the update process, make sure that the WiFi is stable and your watch is plugged in.